Question

Suppose the portfolio of a large institutional investor ‘Ace’ has a beta of 1.5, and the standard deviation of the rate of return on its portfolio is 15 percent. The portfolio of another institutional investor ‘Yankee’ has a beta of 0.7. The market portfolio may be expressed as a portfolio comprising the portfolios of Ace and Yankee, and its Sharpe ratio is 0.8 Suppose there is a firm called ‘Rusty Steel’, whose stock’s beta is 2 and it can borrow at the risk free rate, which is 2.5 percent. Rusty’s equity value is £1.5 million and its debt is £1 million. The present value of Rusty’s tax shield is £0.3 million. Assuming that both CAPM and the Modigliani-Miller theorem with corporate taxes hold, answer the following questions.

b) What is the expected return on the market portfolio? [5 marks] c) What is the standard deviation of the rate of return on Yankee’s portfolio? [5 marks] d) What is the after-tax WACC of Rusty?

Answer 1

b.Expected return of the market porfolio:

As per CAPM:

Expected return=RFR+(Beta*(Market return-RFR))

Using details for 'Ace' & given RFR=2.5%

15%=2.5%+(1.5*(Market return-2.5%))

solving for market return,

we get the expected return on market portfolio as :

10.83%

c.Standard deviation of the rate of return on Yankee's portfolio:

Expected return (Yankee)=2.5%+(0.7*(10.83%-2.5%))

8.33%

So, standard deviation of the rate of return of Yankee from market return =

Sq.rt. Of (ER(Y)-ER(mkt.))^2= ((8.33%-10.83%)^2)^(1/2)=

2.50%

d. After-tax WACC of Rusty

Using CAPM, Cost of equity for Cunning=

ke=RFR+(Beta*(Market Return-RFR))

ie. Ke=2.5%+(2*(10.83%-2.5%))=

19.16%

&

its cost of debt= Its borrowing rate=2.5%

So,

WACC=(Wt.D*kD*(1-Tax Rate))+(Wt.E*kE)

ie.((1/2.5)*2.5%*(1-30%))+((1.5/2.5)*19.16%)=

12.20%